Numerical simulation of electric field-induced concentration patterns at fluid interfaces

Experiments have shown that DNA molecules attached to the liquid-liquid interface of an aqueous two-phase system form concentration patterns when subject to an electric field normal to the interface. Electroosmotic flow due to the Debye layer around the molecules induces the formation and interaction of clusters and connecting filaments. Previous findings have revealed concentration patterns in which shorter-wavelength modes destabilize at later times with progressively faster growth rates. We use a pseudo-spectral Fourier method to solve the governing non-linear integro-differential equation and propose an additional term to account for the crowding of molecules. Simulation results for the pattern formation as well as the interaction and merging of DNA clusters agree well with experimental observations. We further characterize the dynamics by identifying inherent scales for the time of pattern formation and the average distance between clusters.